Consider the eternalist/presentist debate. The eternalist thinks there is a past time with dinosaurs, the presentist thinks there is only the present time, but that it is true at the present time that there were dinosaurs nevertheless. I think the creationist should hold that there are past times only six thousand years into the past, but that it is nevertheless true that prior to this such-and-such was going on. It’s true that there were apes who would evolve into humans; but nevertheless, there are no past apes who are our ancestors.
Trust a philosopher to suck all the empirical content out of a theory! Fun idea, though. Suppose we prefer the intuitive (if incoherent) "moving spotlight" theory of time. Could God create a world with a past that never was present? That is, the full historical timeline is created, but the spotlight of time gets set to start part way through, rather than right at the beginning. That way, perhaps the creationist could even grant that there "are" past apes who are our ancestors, but nevertheless insist that human evolution never really happened. (God skipped his divine spotlight over that unwelcome bit of history.)